Distinction between low-barrier hydrogen bond and ordinary hydrogen bond: a case study of varying nature of charge assisted hydrogen bonds of diglycine perchlorate crystal

Hydrogen bonding is a complex phenomenon that is a resultant of many energy components like the electrostatic, dispersive, covalent, charge cloud overlap repulsion etc, nature of hydrogen bond (H-bond) depends on which of these components play a dominant role. Low barrier hydrogen bond (LBHB) constitutes a special category of hydrogen bonds characterized by near delocalization of proton between donor and acceptor groups of the H- bond unlike an ordinary hydrogen bond (OHB) having proton clearly localized near the donor group. The significance of LBHBs in macromolecular interactions has been highly controversial, despite may attempts the existence and potential importance of protein LBHBs remains debatable. In order to answer questions like whether or not a distinct class of LBHBs exists and if they do exist under what conditions they are formed and how do they behave differently from OHBs, a detailed study of H-bonding in Diglycine Perchlorate (DGPCl) crystal containing five unique hydrogen bonded glycinium-glycine pairs is undertaken. All O-H–O bonds of DGPCl are between the carboxyl (-COOH) and carboxylate (-COO−) groups with slightly different electron distributions resulting in observable variations in the H-bond geometries, this is an indication of varying strength of these short strong H-bonds. It is found that LBHB nature of the five O-H—O bonds between glycinium-glycine pairs (P1-P5) varies as P1 < P4 < P2 < P3 < P5. This study gives an experimental evidence of the existence of LBHBs and demonstrates that the behaviour of LBHBs is very different from that of strong OHBs.


Introduction
Hydrogen bonds are arguably the most enigmatic and versatile intermolecular interactions [1], they play a fundamental role in biochemical processes hence in order to understand the biophysical systems it becomes important to study the nature of these interactions minutely. Nature of hydrogen bonds particularly the strong ones is complex, it is a resultant of many interactions like the electrostatic, dispersive, covalent, charge cloud overlap repulsion etc Low barrier hydrogen bond (LBHB) constitutes a special category of hydrogen bonds characterized [2,3] by near delocalization of proton between donor and acceptor groups of the hydrogen bond, it is assumed that potential energy landscape for these hydrogen bonds has a double minimum form where the barrier height between the two minima is of the order of zero point energy of the proton. Role of LBHB in enzyme studies is an ongoing topic of interest, as LBHB has been proposed to play a major factor in enzyme catalysis through transition state stabilization; these hydrogen bonds can also play a role in proton conductivity within molecular clusters. In order to consider LBHB as a distinct class of hydrogen bond they should have some unique characteristic not present in ordinary hydrogen bonds (OHB) that have proton clearly localized near the donor group. It was shown by Warshel and Papzan [4] that the novel aspect of LBHB is a more covalent character accompanied by a more disperse charge distribution resulting in different energetic especially in response to its environment. It has been proposed earlier [5] that hydrogen bonding and proton transfer reactions can be Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. described by Empirical Valence Bond models involving valence bond states, according to the three-orbital four electron model for hydrogen bond X-H-Y following three valence bond states are involved in the Hamiltonian For ordinary hydrogen bonds with negatively charge acceptor the charge is primarily concentrated at the acceptor end (Y) this corresponds primarily to the resonance structure ψ 1 in contrast for LBHB the charge is spread out because of charge transfer effects hence the situations corresponds more towards the resonance structure ψ 3.
The significance of LBHBs in macromolecular interactions has been highly controversial [6], despite may attempt the existence and potential importance of protein LBHBs remains debatable. One reason for this is that clear experimental evidence of LBHB in macromolecular crystallography is rare since firstly it is proposed to exist in the transition state only which is difficult to crystallize and secondly even the best x-ray structures of macromolecules do not give H atom positions precisely. Hence in order to answer questions like whether or not a distinct class of LBHBs exists and if they do exist under what conditions they are formed and how do they behave differently from OHB one has to fall back to studying small molecular structures proposed to contain LBHBs.
Diglycine perchlorate (DGPCl) is one such small molecular structure that gave us an opportunity to study subtle differences in the nature of short strong hydrogen bonds, the structure contains five unique charge assisted hydrogen bonds [7], each of these hydrogen bonds have the potential to be a LBHB. DGPCl is a crystalline adduct obtained from 2:1 aqueous solution of Glycine and Perchloric [8] acid. Its crystal structure [8] is Triclinic with space group P-1, an asymmetric unit (figure 1) of DGPCl has five strongly hydrogen bonded positively charged glycinium-glycine pairs (P1-P5) and five negatively charged perchlorate ions. Table 1 gives structural details for the five O-H-O hydrogen bonds between the carboxyl (-COOH) and carboxylate (-COO − ) groups of glycinium-glycine pairs of DGPCl at two different crystal temperatures 293 K and 150 K. Carboxyl-Carboxylate supramolecular motifs [9] are important synthon in bimolecular systems, O-H-O bond between the carboxyl and carboxylate groups has the potential to be a LBHB [6] since the primary requirement for the formation of LBHB [4] namely a close matching of pKa values of the donor and acceptor groups can be easily satisfied in this case.

Computation method
In order to obtain the properties like partial atomic charges, bond orders etc for the atoms and bonds of the glycinium-glycine pair PM6 semi-empirical quantum calculation method [10] as implemented in software MOPAC2016 [11] is used. Experimentally obtained molecular geometry of the glycinium-glycine pair is used in the calculation. Table 2   (Gly) is obtained as following: Gly E Gly E Gly Here E(Gly + -Gly), E(Gly + ) and E(Gly) are the calculated values of total energy for the glycinium-glycine pair, glycinium ion and glycine Zwitter ion respectively. It can be observed (table 1) that the H atom in all the five O-H-O bonds of DGPCl is placed asymmetrically resulting in unequal proton sharing between the donor and acceptor molecules. It is known that the extent to which a functional group can be protonated or deprotonated by the hydrogen transfer from/to the environment is determined by its pKa. The pKa values are usually determined experimentally by potentiometric, spectrophotometric, chromatographic, electrophoresis, calorimetric. conductometric, and NMR techniques. Need for accurate estimation of pKa using theoretical methods was felt for cases where the pKa measurements of molecules or part of molecules were difficult by experimental means. Recently Haslek et al [12] have proposed a protocol to theoretically compute the carboxylic acid pKa using the value of atomic charges on carboxylic group atoms, according to this method following equation can be used to get a theoretical estimate of carboxylic acid pKa:

Discussions
When room temperature (293K) structure of DGPCl is looked into closely following subtle structural features are noticed (  the pairs varies much more significantly (within 0.10 Å): It is important to note that contrary to common expectation that stronger hydrogen bonds have smaller O-O separation, in case of DGPCl P5 that has the longest O-O separation has the strongest hydrogen bond moreover it is observed that P1, P4 and P3 have nearly identical O-O separation but their hydrogen bond strength varies significantly. These observations indicate that there are factors other than the donor-acceptor separation that can affect the hydrogen bond strength; one such factor is diffusivity of acceptor electron density; an earlier systematic study of O-H-O hydrogen bonds with different acceptor groups had shown that acceptors with diffusive electron density made stronger hydrogen bonds [12]. Diffusivity of carboxylate group electron density depends directly on its resonance structure, for DGPCl H-bonds it is observed that the resonant nature of acceptor carboxylate group varies (table 2) as following: P1 < P4 < P2 < P3 < P5 which is same as the variation of hydrogen bond strength for the five pairs. This can be taken as an indication that acceptor group electron density might play a role in determining the strength of the O-H-O hydrogen bonds of DGPCl, i.e. higher resonant nature of the acceptor group might lead to stronger H-bond.
Formation of hydrogen bond is accompanied by charge redistributions [13,14], dipolar field created by the donor and acceptor fragments is responsible for most of the intramolecular charge redistribution, in addition to this polarization driven charge redistribution a small amount of charge is transferred locally from acceptor to the donor upon hydrogen bond formation, this gives an estimate of the covalent contribution to the hydrogen bond. The positive charge of bridging H atom increases with hydrogen bond formation, in addition there is a electron density flows from the proton acceptor molecule to the donor, causing a greater negative charge on the donor atom and more positive charge on the acceptor atom. It is observed that for DGPCl the partial charge on the donor oxygen atoms varies as P1 < P4 < P2 < P3 < P5, this leads us to conclude that the covalent contribution to these hydrogen bonds vary as P1 < P4 < P2 < P3 < P5. This conclusion is also supported by the calculated values of O-H bond order reported in table 2. Earlier Ab initio quantum calculations [15] demonstrated that the delocalization index derived from Quantum Chemical Topology (QCT) serves as bond order, hence for a given bond the value of bond order gives a measure of electron sharing. Looking at the bond order values of O-H bonds (table 2) it is concluded that the electron sharing between the H atom and accepter O varies as P1 < P4 < P2 < P3 < P5.
A recent study [16] on pairwise interaction between atoms and its dependence on range of possible distances between the atoms demonstrated that the nature of interaction between H and O atom changes continuously with the distance between them. The authors of this study showed that as the distance between H and O atoms changed the nature of interatomic interaction gradually changed from primarily covalent in the range 0.58-1.36Å to primarily electrostatic in the range 1.36-2.14Å to primarily dispersive in the range 2.14-2. In order to further support our conclusion we tried estimating the pKa difference (ΔPka) between the donor and acceptor groups since the existence of LBHB [4] is possible only for cases where ΔpKa ∼ 0. Table 2 lists the calculated pKa values for the donor and acceptor groups of H-bonds of DGPCl along with the pKa differences at two temperature (293 K & 150 K) . Using the pKa slide rule for hydrogen bonds [17] which states that strong hydrogen bonds that have the potential to be a LBHB have ΔPka in the range −3 to 3, we conclude the hydrogen bonds in pair P5 and P3 are the ones that can belong to LBHB where as the H-bonds of remaining pairs are strong OHBs.  [19]. For ordinary hydrogen bonds shorter O-H segment has covalent nature and the longer O-H segment has electrostatic or dispersive nature, this difference is accounted for in calculation by using different parameter values [20] in potentials describing the two segments. Pressure response for this hydrogen bonded system was shown [20] to be such that O-H bond becomes shorter with pressure and O-H nonbond becomes longer, hydrogen atom remains bonded to original donor atom and there is no pressure induced symmetrisation of such a hydrogen bond. It was demonstrated by Holzapfel [18] that in special cases where both O-H segment and O-H segment posses partial covalent nature as in the case of LBHB, same potentials parameters have to be used to describe the two segments of the hydrogen bond. Pressure response for such a system is very different from that seen in ordinary hydrogen bond described previously, it was shown [18] figure 2(a)). We have searched the CSD using the DRAW option available in ConQuest program [21], only organic crystal structures obtained from single crystal diffraction technique with R-factors less than 5% were considered.  It is interesting to compare the nature [22] of LBHBs to the symmetric double well hydrogen bonds (SDWHB) found in crystals like Triglycine sulphate [23] (TGS) and Potassium Dihydrogen Phosphate [24] (KDP). Although the energy contours for both these types of hydrogen bonds has symmetric double well form the barrier height for SDWHB is high enough to ensure that proton is covalently bonded only to one of the atoms (donor/acceptor), hence SDWHB are ordinary hydrogen bonds with two symmetry equivalent H positions.  [25] have demonstrated that in order to have large proton conductivity presence of SDWHB is required within the material; in contrast presence of LBHB can result in lower conductivity due to partial proton transfer.

Since the difference between the lengths of O-H and H-O segments of O-H-O bonds is larger for SDWHB
The above discussion shows that we can have strong ordinary hydrogen bonds with energy landscape symmetric or asymmetric (SDWHB & ADWHB respectively) depending on the whether the pKa difference between the donor and acceptor is close to zero or non-zero, but in either case the H-atom is primarily covalent bonded to one atom and interacts electrostatically with the other (figures 3(a) and (b)). OHBs found in DGPCl pairs P1, P2 & P4 belong to the category ADWHB where as those found in KDP and TGS crystals belong to the category SDWHB. In Contrast the energy landscape for LBHB is such that H-atom is partially covalently bonded to both donor and acceptor atoms as is seen for the case of H-bond of pair P5.
In order to demonstrate the above mentioned differences between SDWHB, ADWHB and LBHB we have generated the H-bond potential energy contours for the three different types of H-bonds using Diabatic state model [26][27][28] for hydrogen bonds (detailed expression for potential energy used in calculation are given in appendix), for the sake of comparison O-O distance for all the three cases is taken as 2.48Å (figure 3), the difference in shape of the potential is obtained by varying the potential parameters V 0 that takes into account the asymmetry between the donor and acceptor atoms and Δ 1 which is proportion to the overlap of lone pair orbital of acceptor atom with the orbital on the donor. Ground state energy (E 0 ) as well as ground state wavefuction (Ψ 0 ) for the calculated potentials is obtained using the program FINDIF [29]. It is observed that for ordinary hydrogen bonds ADWHB & SDWHB the potential barrier height is significantly higher than the ground state energy (figures 3(a) and (b)), the H-atom wavefunction is largely confined to one potential well, for the symmetric case H-atom hops between the two potential wells resulting in two maxima in the wavefunction, H-atom hopping is purely a classical phenomenon dependent on the sample temperature and H-bond hopping can be stopped by lowering the temperature as seen in case of KDP crystals. However in case of LBHB (figure 3(c)) potential barrier height is of the order of the ground state energy, H-atom wave function is spread over both the wells resulting in H-atom making partial covalent bond with both donor as well as acceptor atoms, this phenomenon will be temperature independent as long as the donor-acceptor distance remains unchanged with temperature.

Conclusion
We started off looking for concrete experimental evidence to answer questions like whether or not a distinct class of hydrogen bonds namely LBHBs exists and if it does exist under what conditions these H-bonds are formed   • Cambridge structural database analysis of general properties of O-H-O bonds between Carboxyl-Carboxylate groups in organic small molecules shows that these H-bonds are mainly electrostatic in nature and only small fraction of these H-bonds that are predominantly covalent in nature belong to the LBHB class.
Based on the above stated conclusions regarding the nature of LBHBs we are now in a much better position to answer the questions we started with, this study gives an experimental evidence of the existence of LBHBs and demonstrates that the behaviour of LBHBs is very different from that of strong OBHs. Unlike OHBs that are very commonly observed in biomolecules LBHBs are rare and wherever present they are expected to fulfil specialized roles, this fact was recently demonstrated by a study by Shaobo Dai et al [30] in which they observed a fluctuating LBHB acting as a switching element in cooperativity pathways of multimeric enzymes.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).

Appendix: Diabatic state model for H-bonding
According to the diabatic model the O-H···O hydrogen bond can be represented by two interacting diabatic states |O-H···O〉 and |O···H-O〉 .The effective Hamiltonian describing the two interacting diabatic states has the form Where V(r) = D[ This model has essentially two free parameters b and Δ 1 .